Homework Sourse1 Fill in each unshaded cell of the following chart with one
1. Fill in each un-shaded cell of the following chart with one of the following: E (empty), F (finite), C (countably infinite), or U (uncountably infinite) to indicate the result of performing the intersection operation between various sets of numbers.
INTERSECTION
N (naturals)
Z (integers)
Q (rationals)
Q’ (irrationals)
R (reals)
N (naturals)
Z (integers)
Q (rationals)
Q’ (irrationals)
R (reals)
| INTERSECTION | N (naturals) | Z (integers) | Q (rationals) | Q’ (irrationals) | R (reals) |
| N (naturals) | |||||
| Z (integers) | |||||
| Q (rationals) | |||||
| Q’ (irrationals) | |||||
| R (reals) |
Solution
natural numbers are countably infinite
integers are countably infinite
rational are countable infinite
irrational are uncountable
Real numbers are uncountable
natural numbers-> 1,2,3...(only positive)
integers->positiive + negative +0
rational-those can be write in ratio
irrational-irrational number is a real number that cannot be expressed as a ratio of integers
real numbers-rational+irrational
| INTERSECTION | N (naturals) | Z (integers) | Q (rationals) | Q’ (irrationals) | R (reals) |
| N (naturals) | C | C | C | E | C |
| Z (integers) | C | C | C | E | C |
| Q (rationals) | C | C | C | E | C |
| Q’ (irrationals) | E | E | E | U | U |
| R (reals) | C | C | C | U | U |
